The National Mathematics Advisory Panel states that learning mathematics requires three types of knowledge:
Factual knowledge and automatic retrieval of basic math facts refers to having ready in memory the answers to a relatively small set of problems of addition, subtraction, multiplication and division.
Procedural Knowledge refers to a sequence of steps by which frequently encountered problems may be solved.
Conceptual knowledge is an understanding of meaning. Students must understand the "why" of mathematical concept.
FACTUAL KNOWLEDGE...covers the facts within the concepts students need to know. This can be learned by memorization and repetition, such as knowing that 2 + 3 = 5. It also refers to memory of specific events and information.
PROCEDURAL KNOWLEDGE...is knowing how to complete an activity or a task using strategy or procedure. For example, knowing how to solve 2 + 3 by continuing to count “3, 4, 5…”
CONCEPTUAL KNOWLEDGE...is the knowledge of how and why a procedure works. For example, knowing that when we count, the last number we say represents how many items are in the set.
Since numeracy involves the application of knowledge in all aspects of daily living, these three aspects of knowledge, which mutually support each other, facilitate learning and understanding in numeracy.
When designing learning tasks, teachers should provide learning opportunities that: allow for application of knowledge make connections to previous learning and experiences are purposeful and authentic enable different possibilities, strategies and products to emerge
To achieve this, teachers need to be aware of how and where numeracy lives in their subject areas, as well as use teachable moments as they occur.
Factual knowledge and automatic retrieval of basic math facts refers to having ready in memory the answers to a relatively small set of problems of addition, subtraction, multiplication and division.
Procedural Knowledge refers to a sequence of steps by which frequently encountered problems may be solved.
Conceptual knowledge is an understanding of meaning. Students must understand the "why" of mathematical concept.
Conceptual understanding:
http://www.ascd.org/publications/books/106008/chapters/Conceptual-Understanding.aspx
Conceptual vs procedural knowledge:
http://teachingmathliteracy.weebly.com/conceptual-vs-procedural-knowledge.html
FACTUAL KNOWLEDGE...covers the facts within the concepts students need to know. This can be learned by memorization and repetition, such as knowing that 2 + 3 = 5. It also refers to memory of specific events and information.
PROCEDURAL KNOWLEDGE...is knowing how to complete an activity or a task using strategy or procedure. For example, knowing how to solve 2 + 3 by continuing to count “3, 4, 5…”
CONCEPTUAL KNOWLEDGE...is the knowledge of how and why a procedure works. For example, knowing that when we count, the last number we say represents how many items are in the set.
Since numeracy involves the application of knowledge in all aspects of daily living, these three aspects of knowledge, which mutually support each other, facilitate learning and understanding in numeracy.
When designing learning tasks, teachers should provide learning opportunities that: allow for application of knowledge make connections to previous learning and experiences are purposeful and authentic enable different possibilities, strategies and products to emerge
To achieve this, teachers need to be aware of how and where numeracy lives in their subject areas, as well as use teachable moments as they occur.
http://erlc.ca/resources/literacy_numeracy_programming/documents/erlc-k-12-numeracy-framework.pdf